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Codimension two bifurcation in a simple delayed neuron model

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Abstract

This paper reports a simple delayed neuron model. Bogdanov-Takens bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at double zero singularity and show that the model can exhibit pitchfork, Hopf, homoclinic bifurcation and saddle node bifurcation of periodic orbits. Some numerical simulations are given to support the analytic results.

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Acknowledgments

The work is supported by the National Natural Science Foundation of China Grant No.60974020 and the Fundamental Research Funds for the Central Universities of China (Project No. CDJZR10 18 55 01), is also supported by NPRP Grant 4-1162-1-181 from the Qatar National Research Fund (a member of the Qatar Foundation).

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Authors and Affiliations

  1. College of Computer Science, Chongqing University, Chongqing, 400030, People’s Republic of China

    Xing He & Chuandong Li

  2. Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

    Tingwen Huang

  3. College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling, Chongqing, 408100, People’s Republic of China

    Mei Peng

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  1. Xing He
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  2. Chuandong Li
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  3. Tingwen Huang
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  4. Mei Peng
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Correspondence to Chuandong Li.

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He, X., Li, C., Huang, T. et al. Codimension two bifurcation in a simple delayed neuron model. Neural Comput & Applic 23, 2295–2300 (2013). https://doi.org/10.1007/s00521-012-1181-1

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  • DOI: https://doi.org/10.1007/s00521-012-1181-1

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